Networks of spiking neurons: the third generation of neural network models

W. Maass


The computational power of formal models for networks of spiking neurons is compared with that of other neural network models based on McCulloch Pitts neurons (i.e., threshold gates), respectively, sigmoidal gates. In particular it is shown that networks of spiking neurons are, with regard to the number of neurons that are needed, computationally more powerful than these other neural network models. A concrete biologically relevant function is exhibited which can be computed by a single spiking neuron (for biologically reasonable values of its parameters), but which requires hundreds of hidden units on a sigmoidal neural net. On the other hand, it is known that any function that can be computed by a small sigmoidal neural net can also be computed by a small network of spiking neurons. This article does not assume prior knowledge about spiking neurons, and it contains an extensive list of references to the currently available literature on computations in networks of spiking neurons and relevant results from neurobiology. ©1997 Elsevier Science Ltd. All rights reserved. Keywords-Spiking neuron, Integrate-and-fire neutron, Computational complexity, Sigmoidal neural nets, Lower bounds.

Reference: W. Maass. Networks of spiking neurons: the third generation of neural network models. Neural Networks, 10:1659-1671, 1997.